Homework Help is Here – Start Your Trial Now!
Math
Advanced Math
(b) Use Euler's method with step size At = 0.5 to approximate this so- lution, and check how close the approximation is to the real solution when t = 2, t = 4, and t = 6.

(b) Use Euler's method with step size At = 0.5 to approximate this so- lution, and check how close the approximation is to the real solution when t = 2, t = 4, and t = 6.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
See similar textbooks
icon
Related questions
Question
100%

I have part A completed but I'm stuck on part B. Are the real solutions the bolded x(t), or are they the x' and y'? Some help would be great thanks!

Consider the system x' = x + 3y y = x - y with initial conditions (0) = 0 and y(0) = 1.² (a) Show that 3 -20 3 +e-2t x(t) = (1² satisfies the initial value problem. (b) Use Euler's method with step size At = 0.5 to approximate this so- lution, and check how close the approximation is to the real solution when t = 2, t = 4, and t = 6. (c) Use Euler's method with step size At = 0.1 to approximate this so- lution, and check how close the approximation is to the real solution when t = 2, t = 4, and t = 6. (d) Discuss how and why the Euler approximations differ from the real solution.
Transcribed Image Text:Consider the system x' = x + 3y y = x - y with initial conditions (0) = 0 and y(0) = 1.² (a) Show that 3 -20 3 +e-2t x(t) = (1² satisfies the initial value problem. (b) Use Euler's method with step size At = 0.5 to approximate this so- lution, and check how close the approximation is to the real solution when t = 2, t = 4, and t = 6. (c) Use Euler's method with step size At = 0.1 to approximate this so- lution, and check how close the approximation is to the real solution when t = 2, t = 4, and t = 6. (d) Discuss how and why the Euler approximations differ from the real solution.
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 3 steps with 3 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
Basic Technical Mathematics
Basic Technical Mathematics
Advanced Math
ISBN:
9780134437705
Author:
Washington
Publisher:
PEARSON
Topology
Topology
Advanced Math
ISBN:
9780134689517
Author:
Munkres, James R.
Publisher:
Pearson,
SEE MORE TEXTBOOKS